Abstract
In this paper, a new integral identity is provided. Based on this equality, Simpson-type dual integral inequalities for functions whose first derivatives are s-convex via Riemann–Liouville fractional integrals are established.
References
[1] M. Alomari, M. Darus and S. S. Dragomir, New inequalities of Simpson’s type for s-convex functions with applications, Res. Rep, Collection 12 (2009), https://vuir.vu.edu.au/id/eprint/17768. Search in Google Scholar
[2] D. Baleanu, A. Kashuri, P. O. Mohammed and B. Meftah, General Raina fractional integral inequalities on coordinates of convex functions, Adv. Difference Equ. 2021 (2021), Paper No. 82. 10.1186/s13662-021-03241-ySearch in Google Scholar
[3] S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, JIPAM. J. Inequal. Pure Appl. Math. 10 (2009), no. 3, Article ID 86. Search in Google Scholar
[4] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, Publ. Inst. Math. (Beograd) (N. S.) 23(37) (1978), 13–20. Search in Google Scholar
[5] T. Chiheb, B. Boulares, M. Imsatfia, B. Meftah and A. Moumen, On s-convexity of dual Simpson type integral inequalities, Symmetry 15 (2023), no. 3, Paper No. 733. 10.3390/sym15030733Search in Google Scholar
[6] T. Chiheb, B. Meftah and A. Dih, Dual Simpson type inequalities for functions whose absolute value of the first derivatives are preinvex, Konuralp J. Math. 10 (2022), no. 1, 73–78. Search in Google Scholar
[7] L. Dedić, M. Matić and J. Pečarić, On dual Euler–Simpson formulae, Bull. Belg. Math. Soc. Simon Stevin 8 (2001), no. 3, 479–504. 10.36045/bbms/1102714571Search in Google Scholar
[8] S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), no. 5, 91–95. 10.1016/S0893-9659(98)00086-XSearch in Google Scholar
[9] S. S. Dragomir, R. P. Agarwal and P. Cerone, On Simpson’s inequality and applications, J. Inequal. Appl. 5 (2000), no. 6, 533–579. 10.1155/S102558340000031XSearch in Google Scholar
[10]
S. Ghomrani, B. Meftah, W. Kaidouchi and M. Benssaad,
Fractional Hermite–Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated
[11] S. Hamida and B. Meftah, Fractional Bullen type inequalities for differentiable preinvex functions, ROMAI J. 16 (2020), no. 2, 63–74. Search in Google Scholar
[12]
W. Kaidouchi, B. Meftah, M. Benssaad and S. Ghomrani,
Fractional Hermite–Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated extended
[13] N. Kamouche, S. Ghomrani and B. Meftah, Fractional Simpson like type inequalities for differentiable s-convex functions, J. Appl. Math. Stat. Inform. 18 (2022), no. 1, 73–91. 10.2478/jamsi-2022-0006Search in Google Scholar
[14] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006. Search in Google Scholar
[15] W. Liu, Ostrowski type fractional integral inequalities for MT-convex functions, Miskolc Math. Notes 16 (2015), no. 1, 249–256. 10.18514/MMN.2015.1131Search in Google Scholar
[16] B. Meftah, Fractional Ostrowski type inequalities for functions whose first derivatives are φ-preinvex, J. Adv. Math. Stud. 10 (2017), no. 3, 335–347. 10.1155/2016/5292603Search in Google Scholar
[17]
B. Meftah,
Fractional Hermite–Hadamard type integral inequalities for functions whose modulus of derivatives are co-ordinated
[18] B. Meftah, M. Benssaad, W. Kaidouchi and S. Ghomrani, Conformable fractional Hermite–Hadamard type inequalities for product of two harmonic s-convex functions, Proc. Amer. Math. Soc. 149 (2021), no. 4, 1495–1506. 10.1090/proc/15396Search in Google Scholar
[19] B. Meftah and A. Lakhdari, Dual Simpson type inequalities for multiplicatively convex functions, Filomat 37 (2023), no. 22, 7673–7683. 10.1090/proc/16292Search in Google Scholar
[20] B. Meftah and K. Mekalfa, Some weighted trapezoidal type inequalities via h-preinvexity, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 24(542) (2020), 81–97. 10.21857/9xn31coznySearch in Google Scholar
[21] B. Meftah, M. Merad, N. Ouanas and A. Souahi, Some new Hermite-Hadamard type inequalities for functions whose nth derivatives are convex, Acta Comment. Univ. Tartu. Math. 23 (2019), no. 2, 163–178. 10.12697/ACUTM.2019.23.15Search in Google Scholar
[22] P. O. Mohammed and T. Abdeljawad, Modification of certain fractional integral inequalities for convex functions, Adv. Difference Equ. 2020 (2020), Paper No. 69. 10.1186/s13662-020-2541-2Search in Google Scholar
[23] P. O. Mohammed and M. Z. Sarikaya, On generalized fractional integral inequalities for twice differentiable convex functions, J. Comput. Appl. Math. 372 (2020), Article ID 112740. 10.1016/j.cam.2020.112740Search in Google Scholar
[24] J. Pečarić and A. Vukelić, General dual Euler–Simpson formulae, J. Math. Inequal. 2 (2008), no. 4, 511–526. 10.7153/jmi-02-46Search in Google Scholar
[25] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Math. Sci. Eng. 187, Academic Press, Boston, 1992. Search in Google Scholar
[26] W. Saleh, B. Meftah and A. Lakhdari, Quantum dual Simpson type inequalities for q-differentiable convex functions, Int. J. Nonlinear Anal. Appl. 14 (2023), no. 4, 63–76. Search in Google Scholar
[27] M. Z. Sarikaya and H. Budak, Generalized Hermite–Hadamard type integral inequalities for fractional integrals, Filomat 30 (2016), no. 5, 1315–1326. 10.2298/FIL1605315SSearch in Google Scholar
[28] M. Z. Sarikaya, E. Set, H. Yaldiz and N. Başak, Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model. 57 (2013), no. 9–10, 2403–2407. 10.1016/j.mcm.2011.12.048Search in Google Scholar
[29] M. Z. Sarikaya and H. Yildirim, On Hermite–Hadamard type inequalities for Riemann–Liouville fractional integrals, Miskolc Math. Notes 17 (2016), no. 2, 1049–1059. 10.18514/MMN.2017.1197Search in Google Scholar
[30] E. Set, M. E. Özdemir and M. Z. Sarıkaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications, Facta Univ. Ser. Math. Inform. 27 (2012), no. 1, 67–82. Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Pseudo-n-multipliers and pseudo-n-Jordan multipliers
- Fractional dual Simpson-type inequalities for differentiable s-convex functions
- Fredholm weighted composition operators between weighted lp spaces: A simple process point of view
- The exterior differential operator on quasi-Kähler manifolds and some relations of its components for smooth functions
- Statistical approximation using wavelets Kantorovich (p,q)-Baskakov operators
- Arzelà’s bounded convergence theorem
- On the Cauchy problem for the generalized double dispersion equation with logarithmic nonlinearity
Articles in the same Issue
- Frontmatter
- Pseudo-n-multipliers and pseudo-n-Jordan multipliers
- Fractional dual Simpson-type inequalities for differentiable s-convex functions
- Fredholm weighted composition operators between weighted lp spaces: A simple process point of view
- The exterior differential operator on quasi-Kähler manifolds and some relations of its components for smooth functions
- Statistical approximation using wavelets Kantorovich (p,q)-Baskakov operators
- Arzelà’s bounded convergence theorem
- On the Cauchy problem for the generalized double dispersion equation with logarithmic nonlinearity